On Marilda Sotomayor's extraordinary contribution to matching theory

Financial support the research grants ECO2012-31962, 2014SGR-142, and ICREA AcademiaWe report on Marilda Sotomayor's extraordinay contribution to Matching Theory on the occasion of her 70th anniversar

Understanding preferences: "demand types", and the existence of equilibrium with indivisibilities

We propose new techniques for understanding agents' valuations. Our classification into \demand types", incorporates existing definitions (substitutes, complements, \strong substitutes", etc.) and permits new ones. Our Unimodularity Theorem generalises previous results about when competitive equilibrium exists for any set of agents whose valuations are all of a \demand type" for indivisible goods. Contrary to popular belief, equilibrium is guaranteed for more classes of purely-complements, than of purely-substitutes, preferences. Our Intersection Count Theorem checks equilibrium existence for combinations of agents with specific valuations by counting the intersection points of geometric objects. Applications include matching and coalition-formation; and the Product-Mix Auction, introduced by the Bank of England in response to the financial crisis

The Hungarian Method for a Mixed Matching Market

We present an algorithm that computes a stable matching in a common generalization of the marriage and the assignment in mathcal{O}(n^4) time

A Survey of Theories of the Family

This review explores the theory of household technology and the associated possibilities for distributing utility among household members. It also explores decision theory within the household, drawing on standard consumer decision theory. The review discusses models of equilbrium in which families are formed by persons voluntarily choosing mates. This theory is analogous to ``Tiebout theory'' in urban economics, where the objects of choice include not only the amount of public goods supplied in each city, but also which individuals live in each place. An aspect of family life that has fewer parallels in the economics of market economies is intrafamilial affection. The final section of this paper reviews a growing theoretical literature on love, altruism and the family.Center for Research on Economic and Social Theory, Department of Economics, University of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/101098/1/ECON082.pd

How (not) to Choose Peers in Studying Groups

This paper analyzes social group formation when agents are subject to peer effects within groups increasing human capital and instantaneous utility. When agents are heterogeneous on two dimensions, ability and social skills, and monetary payments are not feasible the model predicts segregation at the top and at the bottom of the attribute space and bunching for heterogeneous intermediate types. Groups may be heterogeneous in taste types and more heterogeneous types are more likely to participate. The equilibrium allocation does not induce cost-efficient human capital accumulation. Introducing ability tracking may produce beneficial results despite decreasing differences in human capital production.Education, Peer-effects, Matching, Group Formation